Image-forming MR methods which utilize the interaction between magnetic fields and nuclear spins in order to form two-dimensional or three-dimensional images are widely used nowadays, notably in the field of medical diagnostics, because for the imaging of soft tissue they are superior to other imaging methods in many respects, do not require ionizing radiation and are usually not invasive.
According to the MR method in general, the body of the patient to be examined is arranged in a strong, uniform magnetic field whose direction at the same time defines an axis (normally the z-axis) of the co-ordinate system on which the measurement is based. The magnetic field produces different energy levels for the individual nuclear spins in dependence on the magnetic field strength which can be excited (spin resonance) by application of an electromagnetic alternating field (RF field) of defined frequency (so-called Larmor frequency, or MR frequency). From a macroscopic point of view the distribution of the individual nuclear spins produces an overall magnetization which can be deflected out of the state of equilibrium by application of an electromagnetic pulse of appropriate frequency (RF pulse) while the magnetic field extends perpendicular to the z-axis, so that the magnetization performs a precessional motion about the z-axis. The precessional motion describes a surface of a cone whose angle of aperture is referred to as flip angle. The magnitude of the flip angle is dependent on the strength and the duration of the applied electromagnetic pulse. In the case of a so-called 90° pulse, the spins are deflected from the z axis to the transverse plane (flip angle 90°).
After termination of the RF pulse, the magnetization relaxes back to the original state of equilibrium, in which the magnetization in the z direction is built up again with a first time constant T1 (spin lattice or longitudinal relaxation time), and the magnetization in the direction perpendicular to the z direction relaxes with a second time constant T2 (spin-spin or transverse relaxation time). The variation of the magnetization can be detected by means of receiving RF coils which are arranged and oriented within an examination volume of the MR device in such a manner that the variation of the magnetization is measured in the direction perpendicular to the z-axis. The decay of the transverse magnetization is accompanied, after application of, for example, a 90° pulse, by a transition of the nuclear spins (induced by local magnetic field inhomogeneities) from an ordered state with the same phase to a state in which all phase angles are uniformly distributed (dephasing). The dephasing can be compensated by means of a refocusing pulse (for example a 180° pulse). This produces an echo signal (spin echo) in the receiving coils. In order to realize spatial resolution in the body, linear magnetic field gradients extending along the three main axes are superposed on the uniform magnetic field, leading to a linear spatial dependency of the spin resonance frequency. The signal picked up in the receiving coils then contains components of different frequencies which can be associated with different locations in the body. The signal data obtained via the receiving coils corresponds to the spatial frequency domain and is called k-space data. The k-space data usually includes multiple lines acquired with different phase encoding. Each line is digitized by collecting a number of samples. A set of k-space data is converted to an MR image by means of Fourier transformation.
Recently techniques for accelerating MR acquisition have been developed which are called parallel acquisition. Methods in this category are SENSE (Pruessmann et al., “SENSE: Sensitivity Encoding for Fast MRI”, Magnetic Resonance in Medicine 1999, 42 (5), 1952-1962) and SMASH (Sodickson et al., “Simultaneous acquisition of spatial harmonics (SMASH): Fast imaging with radiofrequency coil arrays”, Magnetic Resonance in Medicine 1997, 38, 591-603). SENSE and SMASH use undersampled k-space data acquisition obtained from multiple RF receiving coils in parallel. In these methods, the (complex) signal data from the multiple coils are combined with complex weightings in such a way as to suppress undersampling artifacts (aliasing) in the finally reconstructed MR images. This type of complex array combining is sometimes referred to as spatial filtering, and includes combining which is performed in the k-space domain (as in SMASH) or in the image domain (as in SENSE), as well as methods which are hybrids. In either SENSE or SMASH, it is essential to know the proper weightings or sensitivities of the coils with high accuracy. To obtain the coil sensitivities, i.e. the spatial sensitivity profiles of the array RF coils used for signal detection, a calibration pre-scan is typically performed prior to and/or after the actual image acquisition. In the pre-scan, which is also sometimes referred to as reference scan, the MR signals are usually acquired at a resolution which is significantly lower than the resolution required for the final diagnostic MR image. The low-resolution reference scan consists of an interleaving of signal acquisition via the array RF coils and via a reference coil, usually a volume coil, for example the quadrature body coil of the MR apparatus. Low resolution MR images are reconstructed from the MR signals received via the array RF coils and via the volume RF coil. The coil sensitivities, i.e. the spatial sensitivity profiles of the array RF coils, are then computed by division of the array coil images by the volume coil image.